Computational models, such as those used in modeling geological formations for depth imaging analyses, may need to accurately account for thin singularities, such as salt overhangs, thin lithology beds, down-lap, off-lap, and other phenomena. In general, conventional modeling methods may involve partitioning a space using various surfaces (e.g. horizons, faults, geobodies, etc.) into volumes, and then filling those volumes with various properties (e.g. velocities). In the Computer-Aided Design (CAD) domain, this approach is known as volume or solid modeling and can be achieved by different technologies, including those involving constructive solid geometry, boundary representation, cellular partitioning, and other suitable approaches. Boundary representation models are based on volumes being represented by their frontiers or boundaries, and thus generally rely on mathematical concepts introduced by Requicha (e.g. Representations for Rigid Solids: Theory, Methods and Systems, by Aristides A. G. Requicha, ACM Computing Surveys, December 1980), Mantyla (e.g. Geometric and Solid Modeling: An Introduction, by M. Mantyla, Computer Science Press, 1988), and Hoffman (e.g. Geometric and Solid Modeling: An Introduction, by Christopher M. Hoffman, Morgan Kaufmann, 1989).
The intensive geometrical computations involved in boundary representation modeling depend on the floating point precision of the computer (i.e. round-offs). When performing any mathematical operations such as addition, subtraction, dot product, arithmetic truncations, overflow or underflow, it is possible that the result may require more digits than the variable can hold, leading to a truncation of significant digits. Such truncations may lead to incorrect or inaccurate results that violate the topological consistency of the model. Methods that mitigate the undesirable effects of such truncations may therefore have considerable utility.